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4MA1/1FR Jun 2018, Question 5: Length of a Line Segment

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1FR (Foundation) · Calculator · 5 marks

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The question, in short

Three points A (4, 2), B (1, 4) and C (−1, 1) are plotted on a grid from −5 to 5 in both x and y. Work with a line, a midpoint and a square vertex.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

Plot the straight line x = −3 on the grid and mark it with the letter L.

  1. 1x = −3 means every point on the line has x-coordinate −3
  2. 2So draw a vertical line down the grid at −3 and label it L

AnswerA vertical line through x = −3

Part (b) · 2 marks

Work out the coordinates of the point M lying halfway between A and B.

  1. 1A is (4, 2) and B is (1, 4)
  2. 2Midpoint x = (4 + 1) ÷ 2 = 2.5
  3. 3Midpoint y = (2 + 4) ÷ 2 = 3
  4. 4So M is (2.5, 3)

Answer(2.5, 3)

Part (c) · 2 marks

Given ABCD forms a square, determine the coordinates of the fourth vertex D.

  1. 1A is (4, 2), B is (1, 4) and C is (−1, 1)
  2. 2Going from B to C means 2 left and 3 down
  3. 3Doing the same from A gives D = (4 − 2, 2 − 3) = (2, −1)

Answer(2, −1)

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